The thrust from the two engines on the P-8A is 54,000 lb and max TO weight is 85,000 kg. The total thrust from the four engines on the MPA is 44,800 lb and max TO weight is 80,000 lb. Given these figures I can't see how you can be certain that the MPA will climb faster and arrive in its patrol area sooner.However, the rate of climb is higher for > than 2 engines on any given airplane; hence this new MPA is going to attain optimal cruise altitude sooner than P-8, and it follows that it will arrive to its patrol area before P-8 does. I bet that P-8 can't fly as high as XP-1. The higher the ceiling of jet powered MPA, greater the speed!
http://www.boeing.com/defense-space/military/p8a/docs/P-8A_overview.pdf
IMO, we need to wait for the performance specifications of both aircraft to be made available before we can realistically compare them.
Tas